arXiv subjects

Marco A. R-Monteiro

Publications and source records attributed to Marco A. R-Monteiro.

3 recordsLinked to original sources

arXiv1993

A note on quantum structure constants

The Cartan-Maurer equations for any $q$-group of the $A_{n-1}, B_n, C_n, D_n$ series are given in a convenient form, which allows their direct computation and clarifies their connection with the $q=1$ case. These equations, defining the field strengths, are essential in the construction of $q$-deformed gauge theories. An explicit expression $\om ^i\we \om^j= -\Z {ij}{kl}\om ^k\we \om^l$ for the $q$-commutations of left-invariant one-forms is found, with $\Z{ij}{kl} \om^k \we \om^l \qonelim \om^j\we\om^i$.

hep-th↗

arXiv1993

$q$-Deformed Classical Lie Algebras and their Anyonic Realization

All classical Lie algebras can be realized à la Schwinger in terms of fermionic oscillators. We show that the same can be done for their $q$-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on a two dimensional lattice. The deformation parameter $q$ is a phase related to the anyonic statistical parameter. A crucial rôle in this construction is played by a sort of bosonization formula which gives the generators of the quantum algebras in terms of the underformed ones. The entire procedure works even on one dimensional chains; in such a case $q$ can also be real.

hep-th↗

arXiv1993

Anyonic Realization of $SU_q(N)$ Quantum Algebra

By considering a set of $N$ anyonic oscillators ( non-local, intrinsic two-dimensional objects interpolating between fermionic and bosonic oscillators) on a two-dimensional lattice, we realize the $SU_q(N)$ quantum algebra by means of a generalized Schwinger construction. We find that the deformation parameter $q$ of the algebra is related to the anyonic statistical parameter $ν$ by $q=exp({\rm i}πν)$.

hep-th↗